Abstract: I will outline the proof of a sharp volume comparison theorem and the corresponding rigidity result for compact Kahler manifolds with positive holomorphic sectional curvature. This approach also gives Kewei Zhang's sharp volume estimate for compact Kahler manifolds with positive Ricci curvature.

Bio: Harish Seshadri is currently a professor at the Indian Institute of Science. His research interests include Ricci flow, Einstein manifolds, curvature of Kahler manifolds, and intrinsic metrics in complex analysis.

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